Download Lesson 14: Converting Rational Numbers to Decimals

Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
7•2
Lesson 14: Converting Rational Numbers to Decimals Using Long
Division
Classwork
Example 1: Can All Rational Numbers Be Written as Decimals?
a.
Using the division button on your calculator, explore various quotients of integers 1 through 11. Record your
fraction representations and their corresponding decimal representations in the space below.
b.
What two types of decimals do you see?
Example 2: Decimal Representations of Rational Numbers
In the chart below, organize the fractions and their corresponding decimal representation listed in Example 1 according
to their type of decimal.
What do these fractions have in common?
Lesson 14:
What do these fractions have in common?
Converting Rational Numbers to Decimals Using Long Division
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M2-TE-1.3.0-08.2015
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
7•2
Example 3: Converting Rational Numbers to Decimals Using Long Division
3
4
Use the long division algorithm to find the decimal value of − .
Exercise 1
Convert each rational number to its decimal form using long division.
a.
b.
7
8
− =
3
16
=
Lesson 14:
Converting Rational Numbers to Decimals Using Long Division
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M2-TE-1.3.0-08.2015
S.72
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
7•2
Example 4: Converting Rational Numbers to Decimals Using Long Division
1
Use long division to find the decimal representation of .
3
Exercise 2
Calculate the decimal values of the fraction below using long division. Express your answers using bars over the shortest
sequence of repeating digits.
a.
c.
−
4
9
1
7
Lesson 14:
b.
−
1
11
d.
−
5
6
Converting Rational Numbers to Decimals Using Long Division
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M2-TE-1.3.0-08.2015
S.73
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
7•2
Example 5: Fractions Represent Terminating or Repeating Decimals
How do we determine whether the decimal representation of a quotient of two integers, with the divisor not equal to
zero, will terminate or repeat?
Example 6: Using Rational Number Conversions in Problem Solving
a.
Eric and four of his friends are taking a trip across the New York State Thruway. They decide to split the cost of
tolls equally. If the total cost of tolls is $8, how much will each person have to pay?
b.
Just before leaving on the trip, two of Eric’s friends have a family emergency and cannot go. What is each
person’s share of the $8 tolls now?
Lesson 14:
Converting Rational Numbers to Decimals Using Long Division
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M2-TE-1.3.0-08.2015
S.74
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
7•2
Lesson Summary
The real world requires that we represent rational numbers in different ways depending on the context of a
situation. All rational numbers can be represented as either terminating decimals or repeating decimals using the
long division algorithm. We represent repeating decimals by placing a bar over the shortest sequence of repeating
digits.
Problem Set
1.
Convert each rational number into its decimal form.
1
1
6
9
=
3
=
_______________
2
2
6
=
_______________
3
9
4
3
6
9
=
9
3
=
_______________
4
6
=
_______________
6
9
7
9
5
6
=
=
_______________
=
_______________
=
_______________
=
_______________
=
_______________
=
_______________
=
_______________
_______________
5
2
_______________
_______________
9
1
=
_______________
8
9
One of these decimal representations is not like the others. Why?
Lesson 14:
Converting Rational Numbers to Decimals Using Long Division
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M2-TE-1.3.0-08.2015
S.75
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
7•2
Enrichment:
2.
Chandler tells Aubrey that the decimal value of −
1
is not a repeating decimal. Should Aubrey believe him?
17
Explain.
3.
Complete the quotients below without using a calculator, and answer the questions that follow.
a.
Convert each rational number in the table to its decimal equivalent.
1
=
11
6
=
11
2
=
11
7
=
11
3
=
11
8
=
11
4
=
11
5
=
11
10
=
11
9
=
11
Do you see a pattern? Explain.
b.
Convert each rational number in the table to its decimal equivalent.
0
=
99
10
=
99
62
=
99
58
=
99
20
=
99
77
=
99
30
=
99
81
=
99
45
=
99
98
=
99
Do you see a pattern? Explain.
c.
Can you find other rational numbers that follow similar patterns?
Lesson 14:
Converting Rational Numbers to Decimals Using Long Division
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M2-TE-1.3.0-08.2015
S.76
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.